The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  0  1  1  X  1  1  1  1  1  1  1  X  1  1  1  1 aX  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X (a+1)X  1  1  0 aX  1  1
 0  1  1  a (a+1)X+a+1  0 (a+1)X+1  a (a+1)X+a+1  1  0  a (a+1)X+1  1 (a+1)X+a+1 X+a  1  X (a+1)X+1 aX+a+1 X+a  X  1 aX+a+1  1  X aX+1 a+1 X+a  1  0 aX+1  a aX+a+1  X (a+1)X+a+1 aX+a+1 (a+1)X+a aX a+1 a+1  a a+1 (a+1)X  X (a+1)X+a (a+1)X+a aX (a+1)X+a aX+a (a+1)X+1 (a+1)X+a+1 X+a+1 aX+a+1 (a+1)X+a aX+1 X+a a+1 aX+1 X+a (a+1)X+1 aX+1 aX (a+1)X  1  1  X (a+1)X  1  1 aX+a+1  a
 0  0 (a+1)X  0  X  X (a+1)X  X (a+1)X  X  0  0  X  X  0 (a+1)X aX aX  0 (a+1)X aX (a+1)X aX aX (a+1)X  X  X  0  X (a+1)X (a+1)X (a+1)X  X  0  X (a+1)X (a+1)X  0  0  X  X (a+1)X aX  0 aX (a+1)X aX (a+1)X  0 (a+1)X  0  X  0 aX aX  0 aX aX aX  X  X  0  0  X aX  0  X (a+1)X aX  X  X (a+1)X
 0  0  0  X aX  X aX (a+1)X (a+1)X  0  X (a+1)X  0 aX aX (a+1)X  0  X  0 aX (a+1)X  X  0 aX  0  0 aX (a+1)X  X aX  0 (a+1)X aX  X (a+1)X  0  X aX (a+1)X  0  X aX  X  0 (a+1)X  0 aX (a+1)X  0  X aX (a+1)X  0  0  X (a+1)X  0 (a+1)X aX  0  X  X aX  X (a+1)X aX aX aX  X aX aX (a+1)X

generates a code of length 72 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 208.

Homogenous weight enumerator: w(x)=1x^0+396x^208+264x^209+252x^210+375x^212+888x^213+156x^214+339x^216+132x^218+342x^220+180x^222+198x^224+120x^225+48x^226+99x^228+264x^229+36x^232+3x^240+3x^248

The gray image is a linear code over GF(4) with n=288, k=6 and d=208.
This code was found by Heurico 1.16 in 0.229 seconds.